A uniform disk of radius 0.485 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with same mass as the disk\'s is attached around the disk\'s rim. A tangential force of 0.247 N applied at the rim causes an angular acceleration of 0.125 rad/s2. Find the mass of the disk.
To find the mass of the disk, we can use the equation for the torque (τ) on a rotating object.
The torque (τ) can be calculated as the product of the force (F) applied at the rim and the radius (r) of the disk:
τ = F * r
In this case, the tangential force (F) applied at the rim is given as 0.247 N, and the radius (r) of the disk is given as 0.485 m. Thus, we can calculate the torque (τ).
Next, we can use the equation for the torque (τ) on a uniform disk to relate it to the mass (m) and the angular acceleration (α) of the disk:
τ = (1/2) * m * r^2 * α
Here, the angular acceleration (α) is given as 0.125 rad/s^2, and we can solve for the mass (m) of the disk.
Let's put it all together:
First, calculate the torque (τ) using the given force (F) and radius (r):
τ = F * r
τ = 0.247 N * 0.485 m
Next, rearrange the equation and solve for the mass (m):
τ = (1/2) * m * r^2 * α
m = (2 * τ) / (r^2 * α)
Now, substitute the calculated torque (τ), radius (r), and angular acceleration (α) into the formula to find the mass (m) of the disk.
m = (2 * τ) / (r^2 * α)
m = (2 * 0.247 N * 0.485 m) / (0.485 m^2 * 0.125 rad/s^2)
Use the given values to perform the calculations and find the mass (m).